Physical significance of green function in quantum mechanics?

Answer 1

There are two parts to this. First is, "What is the physical significance of a wave function?" Secondly, "Why do we normalize it?"

To address the first:
In the Wave Formulation of quantum mechanics the wave function describes the state of a system by way of probabilities. Within a wave function all 'knowable' (observable) information is contained, (e.g. position (x), momentum (p), energy (E), ...). Connected to each observable there is a corresponding operator [for momentum: p=-i(hbar)(d/dx)]. When the operator operates onto the wave function it extracts the desired information from it. This information is called the eigenvalue of the observable... This can get lengthy so I'll just leave it there. For more information I suggest reading David Griffith's "Introduction to Quantum Mechanics". A math knowledge of Calculus II should suffice.

To address the second:
Normalization is simply a tool such that since the probability of finding a particle in the range of +/- (infinity) is 100% then by normalizing the wave function we get rid of the terms that muddy up the answer the probability.
An un-normalized wave function is perfectly fine. It has only been adopted by convention to normalize a wave function.

ex. un-normalized wave function (psi is defined as my wave function)
- The integral from minus infinity to positive infinity of |psi|^2 dx = 2pi

ex. normalized wavefunction
- The integral from minus infinity to positive infinity of |psi|^2 dx = 1

Answer 2

The wave function is used to describe the electronic state of a molecule. You then use operators (such as the hamiltonian) to get physical relevance such as momentum or energy. For proofs and such just consult any physical chemistry text book.

When the wave function is squared (that is multiplied by its complex conjugate) it gives the probability of finding the object that is described at any given location.

Answer 3

It has enormous significance.

It basically shows that without looking at something, it is impossible to know for sure where it is.

A good example of the outcomes of this is the Scrödinger's Cat thought experiment.

Also, it has important effects on the nature of nuclear decay

Hope this helps

The Intelligent Fool

Answer 4

There are two parts to this. First is, "What is the physical significance of a wave function?" Secondly, "Why do we normalize it?"

To address the first:
In the Wave Formulation of quantum mechanics the wave function describes the state of a system by way of probabilities. Within a wave function all 'knowable' (observable) information is contained, (e.g. position (x), momentum (p), energy (E), ...). Connected to each observable there is a corresponding operator [for momentum: p=-i(hbar)(d/dx)]. When the operator operates onto the wave function it extracts the desired information from it. This information is called the eigenvalue of the observable... This can get lengthy so I'll just leave it there. For more information I suggest reading David Griffith's "Introduction to Quantum Mechanics". A math knowledge of Calculus II should suffice.

To address the second:
Normalization is simply a tool such that since the probability of finding a particle in the range of +/- (infinity) is 100% then by normalizing the wave function we get rid of the terms that muddy up the answer the probability.
An un-normalized wave function is perfectly fine. It has only been adopted by convention to normalize a wave function.

ex. un-normalized wave function (psi is defined as my wave function)
- The integral from minus infinity to positive infinity of |psi|^2 dx = 2pi

ex. normalized wavefunction
- The integral from minus infinity to positive infinity of |psi|^2 dx = 1

Answer 5

The Green's function in quantum mechanics represents the response of a quantum system to a localized source or perturbation. It provides a way to solve the time-independent Schrödinger equation for a specific boundary condition. The physical significance lies in its ability to provide information about the probability amplitude for a particle to be at a certain position, given a certain initial condition.